Things of Interest ?

by Siegfried "Zig" Herzog

started August 2013

Introducing myself

I obtained my PhD in Mechanical and Aerospace Engineering from Cornell
University in 1985. After a post-doc at Leheigh University and
Penn State University I started my teaching career at the
Mont Alto campus of the
The Pennsylvania State University

After some 24 years of teaching courses in statics, dynamics, strength of
materials and thermodynamics
I decided to retire on a high note (Excellence in teaching award from the
College of
Engineering at PSU in 2012) and co-authoring a paper in prime number theory
(accepted but not published yet) in July of 2013.

Below you find links to material which are partially related to my past work
and partially to my present hobbies. You may contact me on any of the subjects listed below. Comments, questions and suggestions are most welcome, feel free to use either the "Send a Note to Zig" link or my email address.

On the Gaps of adjacent Prime Numbers

Although prime numbers have - as far as I know - no application in engineering
they are by themselves a fascinating subject area, at least to me. Get a list
of all prime numbers up to 10,000 here

Although there are some equations available which produce a large number of
prime numbers these equations cannot be used to predict prime numbers
in general.
A classical example, dating back to Euler, is the equation :

f(n)=n2 + n + 41

which produces prime numbers for each nbetween 0 and 39 (inclusive)
but mingles primes and composite numbers for larger n in seemingly random fashion.

Already a casual observation of the first, let's say hundred, prime numbers reveals that they seem to thin out. Still, it can be proven easily that there are infinitely many of them, see here for a proof due to Euclid (300 B.C.).

Having access to some computational resouces I participated in a research
project on prime numbers which resulted in an
article EMPIRICAL VERIFICATION OF THE EVEN GOLDBACH CONJECTURE AND COMPUTATION OF PRIME GAPS UP TO 4*1018 by
Tomás Oliveira e Silva, Siegfried Herzog and Silvio Pard published in
Math. Comp. 83 (2014), 2033-2060

Click here for more on prime numbers
and gaps between adjacent prime numbers

Linear Equation Systems Solver

Linear equations appear in all types of mathematical problems and general
solvers for them are frequently needed. Of course, mine cannot cover everything
particularily when it comes to efficiency. But the following has served me well
on numerous occasions.

Stirling Engines

Stirling Engines have fascinated me for a long time but I never found enough
time for this hobby. Follow the link below to find out what I have done sofar
which is mostly theoretical stuff. But some of it might be of interest
to the practioner as well.